#include <MMFAdvection.h>

Inheritance diagram for Nektar::MMFAdvection:

Static Public Member Functions
static SolverUtils::EquationSystemSharedPtr	create (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)
	Creates an instance of this class. More...

Static Public Attributes
static std::string	className
	Name of class. More...

Static Public Attributes inherited from Nektar::SolverUtils::UnsteadySystem
static std::string	cmdSetStartTime

static std::string	cmdSetStartChkNum

Protected Member Functions
	MMFAdvection (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)

	~MMFAdvection () override=default

void	v_InitObject (bool DeclareFields=true) override
	Initialise the object. More...

void	WeakDGDirectionalAdvection (const Array< OneD, Array< OneD, NekDouble > > &InField, Array< OneD, Array< OneD, NekDouble > > &OutField)

Array< OneD, NekDouble > &	GetNormalVelocity ()
	Get the normal velocity. More...

void	DoOdeRhs (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray, const NekDouble time)
	Compute the RHS. More...

void	DoOdeProjection (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray, const NekDouble time)
	Compute the projection. More...

void	GetFluxVector (const Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &flux)
	Evaluate the flux at each solution point. More...

void	GetFluxVectorDeAlias (const Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &flux)
	Evaluate the flux at each solution point using dealiasing. More...

void	EvaluateAdvectionVelocity (Array< OneD, Array< OneD, NekDouble > > &velocity)

NekDouble	ComputeCirculatingArclength (const NekDouble zlevel, const NekDouble Rhs)

void	ComputeNablaCdotVelocity (Array< OneD, NekDouble > &vellc)

void	ComputeveldotMF (Array< OneD, Array< OneD, NekDouble > > &veldotMF)

void	AdvectionBellPlane (Array< OneD, NekDouble > &outfield)

void	AdvectionBellSphere (Array< OneD, NekDouble > &outfield)

void	Test2Dproblem (const NekDouble time, Array< OneD, NekDouble > &outfield)

void	Test3Dproblem (const NekDouble time, Array< OneD, NekDouble > &outfield)

void	v_DoSolve () override
	Solves an unsteady problem. More...

void	v_GenerateSummary (SolverUtils::SummaryList &s) override
	Print Summary. More...

void	v_SetInitialConditions (const NekDouble initialtime, bool dumpInitialConditions, const int domain) override

void	v_EvaluateExactSolution (unsigned int field, Array< OneD, NekDouble > &outfield, const NekDouble time) override

Protected Member Functions inherited from Nektar::SolverUtils::MMFSystem
void	SetUpMovingFrames (const Array< OneD, const Array< OneD, NekDouble > > &Anisotropy, const int TangentXelem)

void	CheckMovingFrames (const Array< OneD, const Array< OneD, NekDouble > > &movingframes)

SOLVER_UTILS_EXPORT void	ComputencdotMF ()

SOLVER_UTILS_EXPORT void	ComputeDivCurlMF ()

SOLVER_UTILS_EXPORT void	ComputeMFtrace ()

SOLVER_UTILS_EXPORT void	VectorDotProd (const Array< OneD, const Array< OneD, NekDouble > > &v1, const Array< OneD, const Array< OneD, NekDouble > > &v2, Array< OneD, NekDouble > &v3)

SOLVER_UTILS_EXPORT void	VectorCrossProd (const Array< OneD, const Array< OneD, NekDouble > > &v1, const Array< OneD, const Array< OneD, NekDouble > > &v2, Array< OneD, Array< OneD, NekDouble > > &v3)

SOLVER_UTILS_EXPORT void	VectorCrossProd (const Array< OneD, NekDouble > &v1, const Array< OneD, NekDouble > &v2, Array< OneD, NekDouble > &v3)

SOLVER_UTILS_EXPORT void	ComputeCurl (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray)

SOLVER_UTILS_EXPORT Array< OneD, NekDouble >	CartesianToMovingframes (const Array< OneD, const Array< OneD, NekDouble > > &uvec, unsigned int field)

SOLVER_UTILS_EXPORT void	DeriveCrossProductMF (Array< OneD, Array< OneD, NekDouble > > &CrossProductMF)

SOLVER_UTILS_EXPORT void	ComputeNtimesMF ()

SOLVER_UTILS_EXPORT void	ComputeNtimesFz (const int dir, const Array< OneD, Array< OneD, NekDouble > > &Fwd, const Array< OneD, Array< OneD, NekDouble > > &Bwd, const Array< OneD, const NekDouble > &imFwd, const Array< OneD, const NekDouble > &imBwd, Array< OneD, NekDouble > &outarrayFwd, Array< OneD, NekDouble > &outarrayBwd)

SOLVER_UTILS_EXPORT void	ComputeNtimesF12 (const Array< OneD, Array< OneD, NekDouble > > &Fwd, const Array< OneD, Array< OneD, NekDouble > > &Bwd, const Array< OneD, const NekDouble > &im1Fwd, const Array< OneD, const NekDouble > &im1Bwd, const Array< OneD, const NekDouble > &im2Fwd, const Array< OneD, const NekDouble > &im2Bwd, Array< OneD, NekDouble > &outarrayFwd, Array< OneD, NekDouble > &outarrayBwd)

SOLVER_UTILS_EXPORT void	ComputeNtimestimesdFz (const int dir, const Array< OneD, Array< OneD, NekDouble > > &Fwd, const Array< OneD, Array< OneD, NekDouble > > &Bwd, const Array< OneD, const NekDouble > &imFwd, const Array< OneD, const NekDouble > &imBwd, Array< OneD, NekDouble > &outarrayFwd, Array< OneD, NekDouble > &outarrayBwd)

SOLVER_UTILS_EXPORT void	ComputeNtimestimesdF12 (const Array< OneD, Array< OneD, NekDouble > > &Fwd, const Array< OneD, Array< OneD, NekDouble > > &Bwd, const Array< OneD, const NekDouble > &im1Fwd, const Array< OneD, const NekDouble > &im1Bwd, const Array< OneD, const NekDouble > &im2Fwd, const Array< OneD, const NekDouble > &im2Bwd, Array< OneD, NekDouble > &outarrayFwd, Array< OneD, NekDouble > &outarrayBwd)

SOLVER_UTILS_EXPORT void	CartesianToSpherical (const NekDouble x0j, const NekDouble x1j, const NekDouble x2j, NekDouble &sin_varphi, NekDouble &cos_varphi, NekDouble &sin_theta, NekDouble &cos_theta)

SOLVER_UTILS_EXPORT void	ComputeZimYim (Array< OneD, Array< OneD, NekDouble > > &epsvec, Array< OneD, Array< OneD, NekDouble > > &muvec)

SOLVER_UTILS_EXPORT void	AdddedtMaxwell (const Array< OneD, const Array< OneD, NekDouble > > &physarray, Array< OneD, Array< OneD, NekDouble > > &outarray)

SOLVER_UTILS_EXPORT void	GetMaxwellFluxVector (const int var, const Array< OneD, const Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)

SOLVER_UTILS_EXPORT void	GetMaxwellFlux1D (const int var, const Array< OneD, const Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)

SOLVER_UTILS_EXPORT void	GetMaxwellFlux2D (const int var, const Array< OneD, const Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)

SOLVER_UTILS_EXPORT void	LaxFriedrichMaxwellFlux1D (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxFwd, Array< OneD, Array< OneD, NekDouble > > &numfluxBwd)

SOLVER_UTILS_EXPORT void	UpwindMaxwellFlux1D (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxFwd, Array< OneD, Array< OneD, NekDouble > > &numfluxBwd)

SOLVER_UTILS_EXPORT void	AverageMaxwellFlux1D (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxFwd, Array< OneD, Array< OneD, NekDouble > > &numfluxBwd)

SOLVER_UTILS_EXPORT void	NumericalMaxwellFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxFwd, Array< OneD, Array< OneD, NekDouble > > &numfluxBwd, const NekDouble time=0.0)

SOLVER_UTILS_EXPORT void	NumericalMaxwellFluxTM (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxFwd, Array< OneD, Array< OneD, NekDouble > > &numfluxBwd, const NekDouble time)

SOLVER_UTILS_EXPORT void	NumericalMaxwellFluxTE (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxFwd, Array< OneD, Array< OneD, NekDouble > > &numfluxBwd, const NekDouble time)

SOLVER_UTILS_EXPORT Array< OneD, NekDouble >	GetIncidentField (const int var, const NekDouble time)

SOLVER_UTILS_EXPORT void	Computedemdxicdote ()

SOLVER_UTILS_EXPORT NekDouble	AvgInt (const Array< OneD, const NekDouble > &inarray)

SOLVER_UTILS_EXPORT NekDouble	AvgAbsInt (const Array< OneD, const NekDouble > &inarray)

SOLVER_UTILS_EXPORT NekDouble	AbsIntegral (const Array< OneD, const NekDouble > &inarray)

SOLVER_UTILS_EXPORT NekDouble	RootMeanSquare (const Array< OneD, const NekDouble > &inarray)

SOLVER_UTILS_EXPORT NekDouble	VectorAvgMagnitude (const Array< OneD, const Array< OneD, NekDouble > > &inarray)

SOLVER_UTILS_EXPORT void	GramSchumitz (const Array< OneD, const Array< OneD, NekDouble > > &v1, const Array< OneD, const Array< OneD, NekDouble > > &v2, Array< OneD, Array< OneD, NekDouble > > &outarray, bool KeepTheMagnitude=true)

SOLVER_UTILS_EXPORT void	BubbleSort (Array< OneD, NekDouble > &refarray, Array< OneD, NekDouble > &sortarray)

Protected Member Functions inherited from Nektar::SolverUtils::UnsteadySystem
SOLVER_UTILS_EXPORT	UnsteadySystem (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)
	Initialises UnsteadySystem class members. More...

SOLVER_UTILS_EXPORT void	v_InitObject (bool DeclareField=true) override
	Init object for UnsteadySystem class. More...

SOLVER_UTILS_EXPORT void	v_DoSolve () override
	Solves an unsteady problem. More...

virtual SOLVER_UTILS_EXPORT void	v_PrintStatusInformation (const int step, const NekDouble cpuTime)
	Print Status Information. More...

virtual SOLVER_UTILS_EXPORT void	v_PrintSummaryStatistics (const NekDouble intTime)
	Print Summary Statistics. More...

SOLVER_UTILS_EXPORT void	v_DoInitialise (bool dumpInitialConditions=true) override
	Sets up initial conditions. More...

SOLVER_UTILS_EXPORT void	v_GenerateSummary (SummaryList &s) override
	Print a summary of time stepping parameters. More...

virtual SOLVER_UTILS_EXPORT NekDouble	v_GetTimeStep (const Array< OneD, const Array< OneD, NekDouble > > &inarray)
	Return the timestep to be used for the next step in the time-marching loop. More...

virtual SOLVER_UTILS_EXPORT bool	v_PreIntegrate (int step)

virtual SOLVER_UTILS_EXPORT bool	v_PostIntegrate (int step)

virtual SOLVER_UTILS_EXPORT bool	v_RequireFwdTrans ()

virtual SOLVER_UTILS_EXPORT void	v_SteadyStateResidual (int step, Array< OneD, NekDouble > &L2)

virtual SOLVER_UTILS_EXPORT bool	v_UpdateTimeStepCheck ()

SOLVER_UTILS_EXPORT NekDouble	MaxTimeStepEstimator ()
	Get the maximum timestep estimator for cfl control. More...

SOLVER_UTILS_EXPORT void	CheckForRestartTime (NekDouble &time, int &nchk)

SOLVER_UTILS_EXPORT void	SVVVarDiffCoeff (const Array< OneD, Array< OneD, NekDouble > > vel, StdRegions::VarCoeffMap &varCoeffMap)
	Evaluate the SVV diffusion coefficient according to Moura's paper where it should proportional to h time velocity. More...

SOLVER_UTILS_EXPORT void	DoDummyProjection (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray, const NekDouble time)
	Perform dummy projection. More...

Protected Member Functions inherited from Nektar::SolverUtils::EquationSystem
SOLVER_UTILS_EXPORT	EquationSystem (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)
	Initialises EquationSystem class members. More...

virtual SOLVER_UTILS_EXPORT void	v_InitObject (bool DeclareFeld=true)
	Initialisation object for EquationSystem. More...

virtual SOLVER_UTILS_EXPORT void	v_DoInitialise (bool dumpInitialConditions=true)
	Virtual function for initialisation implementation. More...

virtual SOLVER_UTILS_EXPORT void	v_DoSolve ()
	Virtual function for solve implementation. More...

virtual SOLVER_UTILS_EXPORT NekDouble	v_LinfError (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray)
	Virtual function for the L_inf error computation between fields and a given exact solution. More...

virtual SOLVER_UTILS_EXPORT NekDouble	v_L2Error (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray, bool Normalised=false)
	Virtual function for the L_2 error computation between fields and a given exact solution. More...

virtual SOLVER_UTILS_EXPORT NekDouble	v_H1Error (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray, bool Normalised=false)
	Virtual function for the H_1 error computation between fields and a given exact solution. More...

virtual SOLVER_UTILS_EXPORT void	v_TransCoeffToPhys ()
	Virtual function for transformation to physical space. More...

virtual SOLVER_UTILS_EXPORT void	v_TransPhysToCoeff ()
	Virtual function for transformation to coefficient space. More...

virtual SOLVER_UTILS_EXPORT void	v_GenerateSummary (SummaryList &l)
	Virtual function for generating summary information. More...

virtual SOLVER_UTILS_EXPORT void	v_SetInitialConditions (NekDouble initialtime=0.0, bool dumpInitialConditions=true, const int domain=0)

virtual SOLVER_UTILS_EXPORT void	v_EvaluateExactSolution (unsigned int field, Array< OneD, NekDouble > &outfield, const NekDouble time)

virtual SOLVER_UTILS_EXPORT void	v_Output (void)

virtual SOLVER_UTILS_EXPORT MultiRegions::ExpListSharedPtr	v_GetPressure (void)

virtual SOLVER_UTILS_EXPORT bool	v_NegatedOp (void)
	Virtual function to identify if operator is negated in DoSolve. More...

virtual SOLVER_UTILS_EXPORT void	v_ExtraFldOutput (std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)

Protected Member Functions inherited from Nektar::SolverUtils::AdvectionSystem
SOLVER_UTILS_EXPORT void	v_InitObject (bool DeclareField=true) override
	Initialisation object for EquationSystem. More...

SOLVER_UTILS_EXPORT bool	v_PostIntegrate (int step) override

virtual SOLVER_UTILS_EXPORT Array< OneD, NekDouble >	v_GetMaxStdVelocity (const NekDouble SpeedSoundFactor=1.0)

Protected Attributes
SolverUtils::RiemannSolverSharedPtr	m_riemannSolver

TestType	m_TestType

NekDouble	m_advx

NekDouble	m_advy

NekDouble	m_advz

NekDouble	m_waveFreq

NekDouble	m_RotAngle

NekDouble	m_Mass0

int	m_VelProjection

Array< OneD, Array< OneD, NekDouble > >	m_velocity

Array< OneD, NekDouble >	m_traceVn

Array< OneD, Array< OneD, NekDouble > >	m_veldotMF

Array< OneD, NekDouble >	m_vellc

Protected Attributes inherited from Nektar::SolverUtils::MMFSystem
NekDouble	m_alpha

NekDouble	m_Incfreq

int	m_SmoothFactor

NekDouble	m_SFinit

Array< OneD, Array< OneD, NekDouble > >	m_movingframes

Array< OneD, Array< OneD, NekDouble > >	m_surfaceNormal

Array< OneD, Array< OneD, NekDouble > >	m_ncdotMFFwd

Array< OneD, Array< OneD, NekDouble > >	m_ncdotMFBwd

Array< OneD, Array< OneD, NekDouble > >	m_nperpcdotMFFwd

Array< OneD, Array< OneD, NekDouble > >	m_nperpcdotMFBwd

Array< OneD, Array< OneD, NekDouble > >	m_DivMF

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_CurlMF

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_MFtraceFwd

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_MFtraceBwd

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_ntimesMFFwd

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_ntimesMFBwd

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_ntimes_ntimesMFFwd

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_ntimes_ntimesMFBwd

Array< OneD, Array< OneD, NekDouble > >	m_ZimFwd

Array< OneD, Array< OneD, NekDouble > >	m_ZimBwd

Array< OneD, Array< OneD, NekDouble > >	m_YimFwd

Array< OneD, Array< OneD, NekDouble > >	m_YimBwd

Array< OneD, Array< OneD, NekDouble > >	m_epsvec

Array< OneD, Array< OneD, NekDouble > >	m_muvec

Array< OneD, Array< OneD, NekDouble > >	m_negepsvecminus1

Array< OneD, Array< OneD, NekDouble > >	m_negmuvecminus1

Array< OneD, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > >	m_dedxi_cdot_e

SpatialDomains::GeomMMF	m_MMFdir

Protected Attributes inherited from Nektar::SolverUtils::UnsteadySystem
LibUtilities::TimeIntegrationSchemeSharedPtr	m_intScheme
	Wrapper to the time integration scheme. More...

LibUtilities::TimeIntegrationSchemeOperators	m_ode
	The time integration scheme operators to use. More...

Array< OneD, Array< OneD, NekDouble > >	m_previousSolution
	Storage for previous solution for steady-state check. More...

std::vector< int >	m_intVariables

NekDouble	m_cflSafetyFactor
	CFL safety factor (comprise between 0 to 1). More...

NekDouble	m_CFLGrowth
	CFL growth rate. More...

NekDouble	m_CFLEnd
	Maximun cfl in cfl growth. More...

int	m_abortSteps
	Number of steps between checks for abort conditions. More...

bool	m_explicitDiffusion
	Indicates if explicit or implicit treatment of diffusion is used. More...

bool	m_explicitAdvection
	Indicates if explicit or implicit treatment of advection is used. More...

bool	m_explicitReaction
	Indicates if explicit or implicit treatment of reaction is used. More...

int	m_steadyStateSteps
	Check for steady state at step interval. More...

NekDouble	m_steadyStateTol
	Tolerance to which steady state should be evaluated at. More...

int	m_filtersInfosteps
	Number of time steps between outputting filters information. More...

std::vector< std::pair< std::string, FilterSharedPtr > >	m_filters

bool	m_homoInitialFwd
	Flag to determine if simulation should start in homogeneous forward transformed state. More...

std::ofstream	m_errFile

NekDouble	m_epsilon
	Diffusion coefficient. More...

Protected Attributes inherited from Nektar::SolverUtils::EquationSystem
LibUtilities::CommSharedPtr	m_comm
	Communicator. More...

bool	m_verbose

LibUtilities::SessionReaderSharedPtr	m_session
	The session reader. More...

std::map< std::string, SolverUtils::SessionFunctionSharedPtr >	m_sessionFunctions
	Map of known SessionFunctions. More...

LibUtilities::FieldIOSharedPtr	m_fld
	Field input/output. More...

Array< OneD, MultiRegions::ExpListSharedPtr >	m_fields
	Array holding all dependent variables. More...

SpatialDomains::BoundaryConditionsSharedPtr	m_boundaryConditions
	Pointer to boundary conditions object. More...

SpatialDomains::MeshGraphSharedPtr	m_graph
	Pointer to graph defining mesh. More...

std::string	m_sessionName
	Name of the session. More...

NekDouble	m_time
	Current time of simulation. More...

int	m_initialStep
	Number of the step where the simulation should begin. More...

NekDouble	m_fintime
	Finish time of the simulation. More...

NekDouble	m_timestep
	Time step size. More...

NekDouble	m_lambda
	Lambda constant in real system if one required. More...

NekDouble	m_checktime
	Time between checkpoints. More...

NekDouble	m_lastCheckTime

NekDouble	m_TimeIncrementFactor

int	m_nchk
	Number of checkpoints written so far. More...

int	m_steps
	Number of steps to take. More...

int	m_checksteps
	Number of steps between checkpoints. More...

int	m_infosteps
	Number of time steps between outputting status information. More...

int	m_iterPIT = 0
	Number of parallel-in-time time iteration. More...

int	m_windowPIT = 0
	Index of windows for parallel-in-time time iteration. More...

int	m_spacedim
	Spatial dimension (>= expansion dim). More...

int	m_expdim
	Expansion dimension. More...

bool	m_singleMode
	Flag to determine if single homogeneous mode is used. More...

bool	m_halfMode
	Flag to determine if half homogeneous mode is used. More...

bool	m_multipleModes
	Flag to determine if use multiple homogenenous modes are used. More...

bool	m_useFFT
	Flag to determine if FFT is used for homogeneous transform. More...

bool	m_homogen_dealiasing
	Flag to determine if dealiasing is used for homogeneous simulations. More...

bool	m_specHP_dealiasing
	Flag to determine if dealisising is usde for the Spectral/hp element discretisation. More...

enum MultiRegions::ProjectionType	m_projectionType
	Type of projection; e.g continuous or discontinuous. More...

Array< OneD, Array< OneD, NekDouble > >	m_traceNormals
	Array holding trace normals for DG simulations in the forwards direction. More...

Array< OneD, bool >	m_checkIfSystemSingular
	Flag to indicate if the fields should be checked for singularity. More...

LibUtilities::FieldMetaDataMap	m_fieldMetaDataMap
	Map to identify relevant solver info to dump in output fields. More...

Array< OneD, NekDouble >	m_movingFrameData
	Moving reference frame status in the inertial frame X, Y, Z, Theta_x, Theta_y, Theta_z, U, V, W, Omega_x, Omega_y, Omega_z, A_x, A_y, A_z, DOmega_x, DOmega_y, DOmega_z, pivot_x, pivot_y, pivot_z. More...

std::vector< std::string >	m_strFrameData
	variable name in m_movingFrameData More...

int	m_NumQuadPointsError
	Number of Quadrature points used to work out the error. More...

enum HomogeneousType	m_HomogeneousType

NekDouble	m_LhomX
	physical length in X direction (if homogeneous) More...

NekDouble	m_LhomY
	physical length in Y direction (if homogeneous) More...

NekDouble	m_LhomZ
	physical length in Z direction (if homogeneous) More...

int	m_npointsX
	number of points in X direction (if homogeneous) More...

int	m_npointsY
	number of points in Y direction (if homogeneous) More...

int	m_npointsZ
	number of points in Z direction (if homogeneous) More...

int	m_HomoDirec
	number of homogenous directions More...

Protected Attributes inherited from Nektar::SolverUtils::ALEHelper
Array< OneD, MultiRegions::ExpListSharedPtr >	m_fieldsALE

Array< OneD, Array< OneD, NekDouble > >	m_gridVelocity

Array< OneD, Array< OneD, NekDouble > >	m_gridVelocityTrace

std::vector< ALEBaseShPtr >	m_ALEs

bool	m_ALESolver = false

bool	m_ImplicitALESolver = false

NekDouble	m_prevStageTime = 0.0

int	m_spaceDim

Protected Attributes inherited from Nektar::SolverUtils::AdvectionSystem
SolverUtils::AdvectionSharedPtr	m_advObject
	Advection term. More...

Friends
class	MemoryManager< MMFAdvection >

Additional Inherited Members
Public Member Functions inherited from Nektar::SolverUtils::MMFSystem
SOLVER_UTILS_EXPORT	MMFSystem (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)

SOLVER_UTILS_EXPORT	~MMFSystem () override

SOLVER_UTILS_EXPORT void	v_GenerateSummary (SummaryList &s) override
	Virtual function for generating summary information. More...

SOLVER_UTILS_EXPORT void	MMFInitObject (const Array< OneD, const Array< OneD, NekDouble > > &Anisotropy, const int TangentXelem=-1)

SOLVER_UTILS_EXPORT void	CopyBoundaryTrace (const Array< OneD, const NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd, const BoundaryCopyType BDCopyType, const int var=0, const std::string btype="NoUserDefined")

Public Member Functions inherited from Nektar::SolverUtils::UnsteadySystem
SOLVER_UTILS_EXPORT	~UnsteadySystem () override=default
	Destructor. More...

SOLVER_UTILS_EXPORT NekDouble	GetTimeStep (const Array< OneD, const Array< OneD, NekDouble > > &inarray)
	Calculate the larger time-step mantaining the problem stable. More...

SOLVER_UTILS_EXPORT NekDouble	GetTimeStep ()

SOLVER_UTILS_EXPORT void	SetTimeStep (const NekDouble timestep)

SOLVER_UTILS_EXPORT void	SteadyStateResidual (int step, Array< OneD, NekDouble > &L2)

SOLVER_UTILS_EXPORT LibUtilities::TimeIntegrationSchemeSharedPtr &	GetTimeIntegrationScheme ()
	Returns the time integration scheme. More...

SOLVER_UTILS_EXPORT LibUtilities::TimeIntegrationSchemeOperators &	GetTimeIntegrationSchemeOperators ()
	Returns the time integration scheme operators. More...

Public Member Functions inherited from Nektar::SolverUtils::EquationSystem
virtual SOLVER_UTILS_EXPORT	~EquationSystem ()
	Destructor. More...

SOLVER_UTILS_EXPORT void	InitObject (bool DeclareField=true)
	Initialises the members of this object. More...

SOLVER_UTILS_EXPORT void	DoInitialise (bool dumpInitialConditions=true)
	Perform any initialisation necessary before solving the problem. More...

SOLVER_UTILS_EXPORT void	DoSolve ()
	Solve the problem. More...

SOLVER_UTILS_EXPORT void	TransCoeffToPhys ()
	Transform from coefficient to physical space. More...

SOLVER_UTILS_EXPORT void	TransPhysToCoeff ()
	Transform from physical to coefficient space. More...

SOLVER_UTILS_EXPORT void	Output ()
	Perform output operations after solve. More...

SOLVER_UTILS_EXPORT std::string	GetSessionName ()
	Get Session name. More...

template<class T >
std::shared_ptr< T >	as ()

SOLVER_UTILS_EXPORT void	ResetSessionName (std::string newname)
	Reset Session name. More...

SOLVER_UTILS_EXPORT LibUtilities::SessionReaderSharedPtr	GetSession ()
	Get Session name. More...

SOLVER_UTILS_EXPORT MultiRegions::ExpListSharedPtr	GetPressure ()
	Get pressure field if available. More...

SOLVER_UTILS_EXPORT void	ExtraFldOutput (std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)

SOLVER_UTILS_EXPORT void	PrintSummary (std::ostream &out)
	Print a summary of parameters and solver characteristics. More...

SOLVER_UTILS_EXPORT void	SetLambda (NekDouble lambda)
	Set parameter m_lambda. More...

SOLVER_UTILS_EXPORT SessionFunctionSharedPtr	GetFunction (std::string name, const MultiRegions::ExpListSharedPtr &field=MultiRegions::NullExpListSharedPtr, bool cache=false)
	Get a SessionFunction by name. More...

SOLVER_UTILS_EXPORT void	SetInitialConditions (NekDouble initialtime=0.0, bool dumpInitialConditions=true, const int domain=0)
	Initialise the data in the dependent fields. More...

SOLVER_UTILS_EXPORT void	EvaluateExactSolution (int field, Array< OneD, NekDouble > &outfield, const NekDouble time)
	Evaluates an exact solution. More...

SOLVER_UTILS_EXPORT NekDouble	L2Error (unsigned int field, const Array< OneD, NekDouble > &exactsoln, bool Normalised=false)
	Compute the L2 error between fields and a given exact solution. More...

SOLVER_UTILS_EXPORT NekDouble	L2Error (unsigned int field, bool Normalised=false)
	Compute the L2 error of the fields. More...

SOLVER_UTILS_EXPORT NekDouble	LinfError (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray)
	Linf error computation. More...

SOLVER_UTILS_EXPORT NekDouble	H1Error (unsigned int field, const Array< OneD, NekDouble > &exactsoln, bool Normalised=false)
	Compute the H1 error between fields and a given exact solution. More...

SOLVER_UTILS_EXPORT Array< OneD, NekDouble >	ErrorExtraPoints (unsigned int field)
	Compute error (L2 and L_inf) over an larger set of quadrature points return [L2 Linf]. More...

SOLVER_UTILS_EXPORT void	Checkpoint_Output (const int n)
	Write checkpoint file of m_fields. More...

SOLVER_UTILS_EXPORT void	Checkpoint_Output (const int n, MultiRegions::ExpListSharedPtr &field, std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)
	Write checkpoint file of custom data fields. More...

SOLVER_UTILS_EXPORT void	Checkpoint_BaseFlow (const int n)
	Write base flow file of m_fields. More...

SOLVER_UTILS_EXPORT void	WriteFld (const std::string &outname)
	Write field data to the given filename. More...

SOLVER_UTILS_EXPORT void	WriteFld (const std::string &outname, MultiRegions::ExpListSharedPtr &field, std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)
	Write input fields to the given filename. More...

SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields)
	Input field data from the given file. More...

SOLVER_UTILS_EXPORT void	ImportFldToMultiDomains (const std::string &infile, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields, const int ndomains)
	Input field data from the given file to multiple domains. More...

SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, std::vector< std::string > &fieldStr, Array< OneD, Array< OneD, NekDouble > > &coeffs)
	Output a field. Input field data into array from the given file. More...

SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, MultiRegions::ExpListSharedPtr &pField, std::string &pFieldName)
	Output a field. Input field data into ExpList from the given file. More...

SOLVER_UTILS_EXPORT void	SessionSummary (SummaryList &vSummary)
	Write out a session summary. More...

SOLVER_UTILS_EXPORT Array< OneD, MultiRegions::ExpListSharedPtr > &	UpdateFields ()

SOLVER_UTILS_EXPORT LibUtilities::FieldMetaDataMap &	UpdateFieldMetaDataMap ()
	Get hold of FieldInfoMap so it can be updated. More...

SOLVER_UTILS_EXPORT NekDouble	GetTime ()
	Return final time. More...

SOLVER_UTILS_EXPORT int	GetNcoeffs ()

SOLVER_UTILS_EXPORT int	GetNcoeffs (const int eid)

SOLVER_UTILS_EXPORT int	GetNumExpModes ()

SOLVER_UTILS_EXPORT const Array< OneD, int >	GetNumExpModesPerExp ()

SOLVER_UTILS_EXPORT int	GetNvariables ()

SOLVER_UTILS_EXPORT const std::string	GetVariable (unsigned int i)

SOLVER_UTILS_EXPORT int	GetTraceTotPoints ()

SOLVER_UTILS_EXPORT int	GetTraceNpoints ()

SOLVER_UTILS_EXPORT int	GetExpSize ()

SOLVER_UTILS_EXPORT int	GetPhys_Offset (int n)

SOLVER_UTILS_EXPORT int	GetCoeff_Offset (int n)

SOLVER_UTILS_EXPORT int	GetTotPoints ()

SOLVER_UTILS_EXPORT int	GetTotPoints (int n)

SOLVER_UTILS_EXPORT int	GetNpoints ()

SOLVER_UTILS_EXPORT int	GetSteps ()

SOLVER_UTILS_EXPORT void	SetSteps (const int steps)

SOLVER_UTILS_EXPORT NekDouble	GetTimeStep ()

SOLVER_UTILS_EXPORT void	CopyFromPhysField (const int i, Array< OneD, NekDouble > &output)

SOLVER_UTILS_EXPORT void	CopyToPhysField (const int i, const Array< OneD, const NekDouble > &input)

SOLVER_UTILS_EXPORT Array< OneD, NekDouble > &	UpdatePhysField (const int i)

SOLVER_UTILS_EXPORT void	ZeroPhysFields ()

SOLVER_UTILS_EXPORT void	FwdTransFields ()

SOLVER_UTILS_EXPORT void	SetModifiedBasis (const bool modbasis)

SOLVER_UTILS_EXPORT int	GetCheckpointNumber ()

SOLVER_UTILS_EXPORT void	SetCheckpointNumber (int num)

SOLVER_UTILS_EXPORT int	GetCheckpointSteps ()

SOLVER_UTILS_EXPORT void	SetCheckpointSteps (int num)

SOLVER_UTILS_EXPORT int	GetInfoSteps ()

SOLVER_UTILS_EXPORT void	SetInfoSteps (int num)

SOLVER_UTILS_EXPORT void	SetIterationNumberPIT (int num)

SOLVER_UTILS_EXPORT void	SetWindowNumberPIT (int num)

SOLVER_UTILS_EXPORT Array< OneD, const Array< OneD, NekDouble > >	GetTraceNormals ()

SOLVER_UTILS_EXPORT void	SetTime (const NekDouble time)

SOLVER_UTILS_EXPORT void	SetTimeStep (const NekDouble timestep)

SOLVER_UTILS_EXPORT void	SetInitialStep (const int step)

SOLVER_UTILS_EXPORT void	SetBoundaryConditions (NekDouble time)
	Evaluates the boundary conditions at the given time. More...

SOLVER_UTILS_EXPORT bool	NegatedOp ()
	Identify if operator is negated in DoSolve. More...

Public Member Functions inherited from Nektar::SolverUtils::ALEHelper
virtual	~ALEHelper ()=default

virtual SOLVER_UTILS_EXPORT void	v_ALEInitObject (int spaceDim, Array< OneD, MultiRegions::ExpListSharedPtr > &fields)

SOLVER_UTILS_EXPORT void	InitObject (int spaceDim, Array< OneD, MultiRegions::ExpListSharedPtr > &fields)

virtual SOLVER_UTILS_EXPORT void	v_UpdateGridVelocity (const NekDouble &time)

virtual SOLVER_UTILS_EXPORT void	v_ALEPreMultiplyMass (Array< OneD, Array< OneD, NekDouble > > &fields)

SOLVER_UTILS_EXPORT void	ALEDoElmtInvMass (Array< OneD, Array< OneD, NekDouble > > &traceNormals, Array< OneD, Array< OneD, NekDouble > > &fields, NekDouble time)
	Update m_fields with u^n by multiplying by inverse mass matrix. That's then used in e.g. checkpoint output and L^2 error calculation. More...

SOLVER_UTILS_EXPORT void	ALEDoElmtInvMassBwdTrans (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray)

SOLVER_UTILS_EXPORT void	MoveMesh (const NekDouble &time, Array< OneD, Array< OneD, NekDouble > > &traceNormals)

const Array< OneD, const Array< OneD, NekDouble > > &	GetGridVelocity ()

SOLVER_UTILS_EXPORT const Array< OneD, const Array< OneD, NekDouble > > &	GetGridVelocityTrace ()

SOLVER_UTILS_EXPORT void	ExtraFldOutputGridVelocity (std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)

Public Member Functions inherited from Nektar::SolverUtils::AdvectionSystem
SOLVER_UTILS_EXPORT	AdvectionSystem (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)

SOLVER_UTILS_EXPORT	~AdvectionSystem () override=default

SOLVER_UTILS_EXPORT AdvectionSharedPtr	GetAdvObject ()
	Returns the advection object held by this instance. More...

SOLVER_UTILS_EXPORT Array< OneD, NekDouble >	GetElmtCFLVals (const bool FlagAcousticCFL=true)

SOLVER_UTILS_EXPORT NekDouble	GetCFLEstimate (int &elmtid)

Public Attributes inherited from Nektar::SolverUtils::MMFSystem
NekDouble	m_pi

int	m_shapedim

SurfaceType	m_surfaceType

UpwindType	m_upwindType

TestMaxwellType	m_TestMaxwellType

PolType	m_PolType

IncType	m_IncType

Array< OneD, NekDouble >	m_MMFfactors

Protected Types inherited from Nektar::SolverUtils::EquationSystem
enum	HomogeneousType { eHomogeneous1D , eHomogeneous2D , eHomogeneous3D , eNotHomogeneous }
	Parameter for homogeneous expansions. More...

Static Protected Attributes inherited from Nektar::SolverUtils::EquationSystem
static std::string	equationSystemTypeLookupIds []

static std::string	projectionTypeLookupIds []

Detailed Description

Definition at line 62 of file MMFAdvection.h.

Constructor & Destructor Documentation

◆ MMFAdvection()

Nektar::MMFAdvection::MMFAdvection	(	const LibUtilities::SessionReaderSharedPtr &	pSession,
		const SpatialDomains::MeshGraphSharedPtr &	pGraph
	)

protected

Definition at line 51 of file MMFAdvection.cpp.

    : UnsteadySystem(pSession, pGraph), MMFSystem(pSession, pGraph),
      AdvectionSystem(pSession, pGraph)
{
}

◆ ~MMFAdvection()

Nektar::MMFAdvection::~MMFAdvection ( )

overrideprotecteddefault

Member Function Documentation

◆ AdvectionBellPlane()

void Nektar::MMFAdvection::AdvectionBellPlane ( Array< OneD, NekDouble > & outfield )

protected

Definition at line 902 of file MMFAdvection.cpp.

{
    int nq = m_fields[0]->GetNpoints();
 
    NekDouble dist, m_radius_limit;
 
    Array<OneD, NekDouble> x(nq);
    Array<OneD, NekDouble> y(nq);
    Array<OneD, NekDouble> z(nq);
 
    m_fields[0]->GetCoords(x, y, z);
 
    // Sets of parameters
    m_radius_limit = 0.5;
 
    NekDouble x0j, x1j;
    outfield = Array<OneD, NekDouble>(nq, 0.0);
    for (int j = 0; j < nq; ++j)
    {
        x0j = x[j];
        x1j = y[j];
 
        dist = sqrt(x0j * x0j + x1j * x1j);
 
        if (dist < m_radius_limit)
        {
            outfield[j] = 0.5 * (1.0 + cos(m_pi * dist / m_radius_limit));
        }
        else
        {
            outfield[j] = 0.0;
        }
    }
}

References Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::MMFSystem::m_pi, tinysimd::sqrt(), and Nektar::UnitTests::z().

Referenced by v_EvaluateExactSolution(), and v_SetInitialConditions().

◆ AdvectionBellSphere()

void Nektar::MMFAdvection::AdvectionBellSphere ( Array< OneD, NekDouble > & outfield )

protected

Definition at line 937 of file MMFAdvection.cpp.

{
    int nq = m_fields[0]->GetNpoints();
 
    NekDouble dist, radius, cosdiff, sin_theta, cos_theta, sin_varphi,
        cos_varphi;
    NekDouble m_theta_c, m_varphi_c, m_radius_limit, m_c0;
 
    Array<OneD, NekDouble> x(nq);
    Array<OneD, NekDouble> y(nq);
    Array<OneD, NekDouble> z(nq);
 
    m_fields[0]->GetCoords(x, y, z);
 
    // Sets of parameters
    m_theta_c      = 0.0;
    m_varphi_c     = 3.0 * m_pi / 2.0;
    m_radius_limit = 7.0 * m_pi / 64.0;
    m_c0           = 0.0;
 
    NekDouble x0j, x1j, x2j;
    outfield = Array<OneD, NekDouble>(nq, 0.0);
    for (int j = 0; j < nq; ++j)
    {
        x0j = x[j];
        x1j = y[j];
        x2j = z[j];
 
        radius = sqrt(x0j * x0j + x1j * x1j + x2j * x2j);
 
        sin_varphi = x1j / sqrt(x0j * x0j + x1j * x1j);
        cos_varphi = x0j / sqrt(x0j * x0j + x1j * x1j);
 
        sin_theta = x2j / radius;
        cos_theta = sqrt(x0j * x0j + x1j * x1j) / radius;
 
        cosdiff = cos_varphi * cos(m_varphi_c) + sin_varphi * sin(m_varphi_c);
        dist    = radius * acos(sin(m_theta_c) * sin_theta +
                                cos(m_theta_c) * cos_theta * cosdiff);
 
        if (dist < m_radius_limit)
        {
            outfield[j] =
                0.5 * (1.0 + cos(m_pi * dist / m_radius_limit)) + m_c0;
        }
        else
        {
            outfield[j] = m_c0;
        }
    }
}

References Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::MMFSystem::m_pi, tinysimd::sqrt(), and Nektar::UnitTests::z().

Referenced by v_EvaluateExactSolution(), and v_SetInitialConditions().

◆ ComputeCirculatingArclength()

NekDouble Nektar::MMFAdvection::ComputeCirculatingArclength	(	const NekDouble	zlevel,
		const NekDouble	Rhs
	)

protected

Definition at line 679 of file MMFAdvection.cpp.

{
 
    NekDouble Tol = 0.0001, Maxiter = 1000, N = 100;
    NekDouble newy, F = 0.0, dF = 1.0, y0, tmp;
 
    Array<OneD, NekDouble> xp(N + 1);
    Array<OneD, NekDouble> yp(N + 1);
 
    NekDouble intval = 0.0;
    switch (m_surfaceType)
    {
        case SolverUtils::eSphere:
        case SolverUtils::eTRSphere:
        {
            intval = sqrt(Rhs - zlevel * zlevel);
        }
        break;
 
        case SolverUtils::eIrregular:
        {
            intval = sqrt(0.5 * (Rhs - zlevel * zlevel * zlevel * zlevel -
                                 zlevel * zlevel));
        }
        break;
 
        case SolverUtils::eNonconvex:
        {
            tmp = 0.5 *
                  (Rhs - zlevel * zlevel * zlevel * zlevel - zlevel * zlevel);
            intval = sqrt(0.5 * (1.0 + sqrt(1.0 + 4.0 * tmp)));
        }
        break;
 
        default:
            break;
    }
 
    switch (m_surfaceType)
    {
        // Find the half of all the xp and yp on zlevel ....
        case SolverUtils::eSphere:
        case SolverUtils::eTRSphere:
        case SolverUtils::eIrregular:
        {
            for (int j = 0; j < N + 1; ++j)
            {
                xp[j] = j * 2.0 * intval / N - intval;
 
                y0 = 1.0;
                for (int i = 0; i < Maxiter; ++i)
                {
                    switch (m_surfaceType)
                    {
                        // Find the half of all the xp and yp on zlevel ....
                        case SolverUtils::eSphere:
                        case SolverUtils::eTRSphere:
                        {
                            F = xp[j] * xp[j] + y0 * y0 + zlevel * zlevel - Rhs;
                            dF = 2.0 * y0;
                        }
                        break;
 
                        case SolverUtils::eIrregular:
                        {
                            F = 2.0 * xp[j] * xp[j] + y0 * y0 * y0 * y0 +
                                y0 * y0 + zlevel * zlevel * zlevel * zlevel +
                                zlevel * zlevel - Rhs;
                            dF = 4.0 * y0 * y0 * y0 + 2.0 * y0;
                        }
                        break;
 
                        default:
                            break;
                    }
 
                    newy = y0 - F / dF;
 
                    if (fabs(F / dF) < Tol)
                    {
                        yp[j] = newy;
                        break;
                    }
 
                    else
                    {
                        y0 = newy;
                    }
 
                    ASSERTL0(i < Maxiter,
                             "Advection Velocity convergence fails");
 
                } // i-loop
            }
        }
        break;
 
        case SolverUtils::eNonconvex:
        {
            for (int j = 0; j < N + 1; ++j)
            {
                xp[j] = j * 2.0 * intval / N - intval;
                tmp   = 0.5 * Rhs -
                      0.5 * (zlevel * zlevel * zlevel * zlevel +
                             zlevel * zlevel) -
                      (xp[j] * xp[j] * xp[j] * xp[j] - xp[j] * xp[j]);
                if (tmp < 0)
                {
                    tmp = -1.0 * tmp;
                }
                yp[j] = sqrt(tmp);
            } // j-loop
        }
        break;
 
        default:
            break;
 
    } // switch-loop
 
    NekDouble pi        = 3.14159265358979323846;
    NekDouble arclength = 0.0;
    for (int j = 0; j < N; ++j)
    {
        arclength =
            arclength + sqrt((yp[j + 1] - yp[j]) * (yp[j + 1] - yp[j]) +
                             (xp[j + 1] - xp[j]) * (xp[j + 1] - xp[j])) /
                            pi;
    }
 
    return arclength;
}

References ASSERTL0, Nektar::SolverUtils::eIrregular, Nektar::SolverUtils::eNonconvex, Nektar::SolverUtils::eSphere, Nektar::SolverUtils::eTRSphere, Nektar::SolverUtils::MMFSystem::m_surfaceType, and tinysimd::sqrt().

◆ ComputeNablaCdotVelocity()

void Nektar::MMFAdvection::ComputeNablaCdotVelocity ( Array< OneD, NekDouble > & vellc )

protected

Definition at line 1034 of file MMFAdvection.cpp.

{
    int nq = m_fields[0]->GetNpoints();
 
    Array<OneD, NekDouble> velcoeff(nq, 0.0);
 
    Array<OneD, NekDouble> Dtmp0(nq);
    Array<OneD, NekDouble> Dtmp1(nq);
    Array<OneD, NekDouble> Dtmp2(nq);
    Array<OneD, NekDouble> Drv(nq);
 
    vellc = Array<OneD, NekDouble>(nq, 0.0);
 
    // m_vellc = \nabla m_vel \cdot tan_i
    Array<OneD, NekDouble> tmp(nq);
    Array<OneD, NekDouble> vessel(nq);
 
    for (int j = 0; j < m_shapedim; ++j)
    {
        Vmath::Zero(nq, velcoeff, 1);
        for (int k = 0; k < m_spacedim; ++k)
        {
            // a_j = tan_j cdot m_vel
            Vmath::Vvtvp(nq, &m_movingframes[j][k * nq], 1, &m_velocity[k][0],
                         1, &velcoeff[0], 1, &velcoeff[0], 1);
        }
 
        // d a_j / d x^k
        m_fields[0]->PhysDeriv(velcoeff, Dtmp0, Dtmp1, Dtmp2);
 
        for (int k = 0; k < m_spacedim; ++k)
        {
            // tan_j^k ( d a_j / d x^k )
            switch (k)
            {
                case (0):
                {
                    Vmath::Vvtvp(nq, &Dtmp0[0], 1, &m_movingframes[j][k * nq],
                                 1, &vellc[0], 1, &vellc[0], 1);
                }
                break;
 
                case (1):
                {
                    Vmath::Vvtvp(nq, &Dtmp1[0], 1, &m_movingframes[j][k * nq],
                                 1, &vellc[0], 1, &vellc[0], 1);
                }
                break;
 
                case (2):
                {
                    Vmath::Vvtvp(nq, &Dtmp2[0], 1, &m_movingframes[j][k * nq],
                                 1, &vellc[0], 1, &vellc[0], 1);
                }
                break;
            }
        }
    }
}

References Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::MMFSystem::m_movingframes, Nektar::SolverUtils::MMFSystem::m_shapedim, Nektar::SolverUtils::EquationSystem::m_spacedim, m_velocity, Vmath::Vvtvp(), and Vmath::Zero().

Referenced by v_InitObject().

◆ ComputeveldotMF()

void Nektar::MMFAdvection::ComputeveldotMF ( Array< OneD, Array< OneD, NekDouble > > & veldotMF )

protected

Definition at line 1094 of file MMFAdvection.cpp.

{
    int nq = m_fields[0]->GetNpoints();
 
    veldotMF = Array<OneD, Array<OneD, NekDouble>>(m_shapedim);
 
    Array<OneD, NekDouble> magMF(nq);
    for (int j = 0; j < m_shapedim; ++j)
    {
        veldotMF[j] = Array<OneD, NekDouble>(nq, 0.0);
 
        for (int k = 0; k < m_spacedim; ++k)
        {
            Vmath::Vvtvp(nq, &m_movingframes[j][k * nq], 1, &m_velocity[k][0],
                         1, &veldotMF[j][0], 1, &veldotMF[j][0], 1);
        }
    }
}

References Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::MMFSystem::m_movingframes, Nektar::SolverUtils::MMFSystem::m_shapedim, Nektar::SolverUtils::EquationSystem::m_spacedim, m_velocity, and Vmath::Vvtvp().

Referenced by v_InitObject().

◆ create()

static SolverUtils::EquationSystemSharedPtr Nektar::MMFAdvection::create	(	const LibUtilities::SessionReaderSharedPtr &	pSession,
		const SpatialDomains::MeshGraphSharedPtr &	pGraph
	)

inlinestatic

Creates an instance of this class.

Definition at line 69 of file MMFAdvection.h.

    {
        SolverUtils::EquationSystemSharedPtr p =
            MemoryManager<MMFAdvection>::AllocateSharedPtr(pSession, pGraph);
        p->InitObject();
        return p;
    }

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), and CellMLToNektar.cellml_metadata::p.

◆ DoOdeProjection()

void Nektar::MMFAdvection::DoOdeProjection	(	const Array< OneD, const Array< OneD, NekDouble > > &	inarray,
		Array< OneD, Array< OneD, NekDouble > > &	outarray,
		const NekDouble	time
	)

protected

Compute the projection.

Compute the projection for the linear advection equation.

Parameters

inarray	Given fields.
outarray	Calculated solution.
time	Time.

Definition at line 448 of file MMFAdvection.cpp.

{
    // Counter variable
    int i;
 
    // Number of fields (variables of the problem)
    int nVariables = inarray.size();
 
    // Set the boundary conditions
    SetBoundaryConditions(time);
 
    // Switch on the projection type (Discontinuous or Continuous)
    switch (m_projectionType)
    {
        // Discontinuous projection
        case MultiRegions::eDiscontinuous:
        {
            // Number of quadrature points
            int nQuadraturePts = GetNpoints();
 
            // Just copy over array
            if (inarray != outarray)
            {
                for (i = 0; i < nVariables; ++i)
                {
                    Vmath::Vcopy(nQuadraturePts, inarray[i], 1, outarray[i], 1);
                }
            }
            break;
        }
 
        // Continuous projection
        case MultiRegions::eGalerkin:
        case MultiRegions::eMixed_CG_Discontinuous:
        {
            Array<OneD, NekDouble> coeffs(m_fields[0]->GetNcoeffs(), 0.0);
            for (i = 0; i < nVariables; ++i)
            {
                m_fields[i]->FwdTrans(inarray[i], coeffs);
                m_fields[i]->BwdTrans(coeffs, outarray[i]);
            }
            break;
        }
 
        default:
            ASSERTL0(false, "Unknown projection scheme");
            break;
    }
}

References ASSERTL0, Nektar::MultiRegions::eDiscontinuous, Nektar::MultiRegions::eGalerkin, Nektar::MultiRegions::eMixed_CG_Discontinuous, Nektar::SolverUtils::EquationSystem::GetNcoeffs(), Nektar::SolverUtils::EquationSystem::GetNpoints(), Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::EquationSystem::m_projectionType, Nektar::SolverUtils::EquationSystem::SetBoundaryConditions(), and Vmath::Vcopy().

Referenced by v_InitObject().

◆ DoOdeRhs()

void Nektar::MMFAdvection::DoOdeRhs	(	const Array< OneD, const Array< OneD, NekDouble > > &	inarray,
		Array< OneD, Array< OneD, NekDouble > > &	outarray,
		const NekDouble	time
	)

protected

Compute the RHS.

Compute the right-hand side for the linear advection equation.

Parameters

inarray	Given fields.
outarray	Calculated solution.
time	Time.

Definition at line 385 of file MMFAdvection.cpp.

{
    int i;
    int nvariables = inarray.size();
    int npoints    = GetNpoints();
 
    switch (m_projectionType)
    {
        case MultiRegions::eDiscontinuous:
        {
            int ncoeffs = inarray[0].size();
 
            if (m_spacedim == 3)
            {
                Array<OneD, Array<OneD, NekDouble>> WeakAdv(nvariables);
 
                WeakAdv[0] = Array<OneD, NekDouble>(ncoeffs * nvariables);
                for (i = 1; i < nvariables; ++i)
                {
                    WeakAdv[i] = WeakAdv[i - 1] + ncoeffs;
                }
 
                // Compute \nabla \cdot \vel u according to MMF scheme
                WeakDGDirectionalAdvection(inarray, WeakAdv);
 
                for (i = 0; i < nvariables; ++i)
                {
                    m_fields[i]->MultiplyByElmtInvMass(WeakAdv[i], WeakAdv[i]);
                    m_fields[i]->BwdTrans(WeakAdv[i], outarray[i]);
                    Vmath::Neg(npoints, outarray[i], 1);
                }
            }
            else
            {
                m_advObject->Advect(2, m_fields, m_velocity, inarray, outarray,
                                    0.0);
 
                for (i = 0; i < nvariables; ++i)
                {
                    Vmath::Neg(npoints, outarray[i], 1);
                }
            }
        }
        break;
 
        default:
        {
            ASSERTL0(false, "Unknown projection scheme");
        }
        break;
    }
}

References ASSERTL0, Nektar::MultiRegions::eDiscontinuous, Nektar::SolverUtils::EquationSystem::GetNpoints(), Nektar::SolverUtils::AdvectionSystem::m_advObject, Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::EquationSystem::m_projectionType, Nektar::SolverUtils::EquationSystem::m_spacedim, m_velocity, Vmath::Neg(), and WeakDGDirectionalAdvection().

Referenced by v_InitObject().

◆ EvaluateAdvectionVelocity()

void Nektar::MMFAdvection::EvaluateAdvectionVelocity ( Array< OneD, Array< OneD, NekDouble > > & velocity )

protected

Definition at line 597 of file MMFAdvection.cpp.

{
    int nq = m_fields[0]->GetNpoints();
 
    NekDouble vel_phi, vel_theta, sin_varphi, cos_varphi, sin_theta, cos_theta;
    NekDouble x0j, x1j, x2j;
 
    Array<OneD, NekDouble> x0(nq);
    Array<OneD, NekDouble> x1(nq);
    Array<OneD, NekDouble> x2(nq);
 
    m_fields[0]->GetCoords(x0, x1, x2);
 
    // theta = a*sin(z/r),  phi = a*tan(y/x);
    for (int j = 0; j < nq; j++)
    {
        x0j = x0[j];
        x1j = x1[j];
        x2j = x2[j];
 
        CartesianToSpherical(x0j, x1j, x2j, sin_varphi, cos_varphi, sin_theta,
                             cos_theta);
 
        vel_phi   = m_waveFreq * (cos_theta * cos(m_RotAngle) +
                                sin_theta * cos_varphi * sin(m_RotAngle));
        vel_theta = -1.0 * m_waveFreq * sin_theta * sin(m_RotAngle);
 
        velocity[0][j] =
            -1.0 * vel_phi * sin_varphi - vel_theta * sin_theta * cos_varphi;
        velocity[1][j] =
            vel_phi * cos_varphi - vel_theta * sin_theta * sin_varphi;
        velocity[2][j] = vel_theta * cos_theta;
    }
 
    // Project the veloicty on the tangent plane
 
    if (m_VelProjection)
    {
        // Check MovingFrames \cdot SurfaceNormals = 0
        Array<OneD, Array<OneD, NekDouble>> newvelocity(m_spacedim);
 
        Array<OneD, Array<OneD, NekDouble>> MF1(m_spacedim);
        Array<OneD, Array<OneD, NekDouble>> MF2(m_spacedim);
        Array<OneD, Array<OneD, NekDouble>> SN(m_spacedim);
 
        for (int k = 0; k < m_spacedim; ++k)
        {
            newvelocity[k] = Array<OneD, NekDouble>(nq);
            MF1[k]         = Array<OneD, NekDouble>(nq);
            MF2[k]         = Array<OneD, NekDouble>(nq);
            SN[k]          = Array<OneD, NekDouble>(nq);
 
            Vmath::Vcopy(nq, &m_movingframes[0][k * nq], 1, &MF1[k][0], 1);
            Vmath::Vcopy(nq, &m_movingframes[1][k * nq], 1, &MF2[k][0], 1);
        }
 
        VectorCrossProd(MF1, MF2, SN);
        GramSchumitz(SN, m_velocity, newvelocity, true);
 
        Array<OneD, NekDouble> tmp(nq, 0.0);
        Array<OneD, NekDouble> Projection(nq, 0.0);
 
        for (int k = 0; k < m_spacedim; ++k)
        {
            Vmath::Vsub(nq, &m_velocity[0][0], 1, &newvelocity[0][0], 1,
                        &tmp[0], 1);
            Vmath::Vmul(nq, &tmp[0], 1, &tmp[0], 1, &tmp[0], 1);
            Vmath::Vadd(nq, tmp, 1, Projection, 1, Projection, 1);
        }
 
        std::cout
            << "Velocity vector is projected onto the tangent plane: Diff = "
            << RootMeanSquare(Projection) << std::endl;
 
        for (int k = 0; k < m_spacedim; ++k)
        {
            Vmath::Vcopy(nq, &newvelocity[k][0], 1, &m_velocity[k][0], 1);
        }
    }
}

References Nektar::SolverUtils::MMFSystem::CartesianToSpherical(), Nektar::SolverUtils::MMFSystem::GramSchumitz(), Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::MMFSystem::m_movingframes, m_RotAngle, Nektar::SolverUtils::EquationSystem::m_spacedim, m_velocity, m_VelProjection, m_waveFreq, Nektar::SolverUtils::MMFSystem::RootMeanSquare(), Vmath::Vadd(), Vmath::Vcopy(), Nektar::SolverUtils::MMFSystem::VectorCrossProd(), Vmath::Vmul(), and Vmath::Vsub().

Referenced by v_InitObject().

◆ GetFluxVector()

void Nektar::MMFAdvection::GetFluxVector	(	const Array< OneD, Array< OneD, NekDouble > > &	physfield,
		Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &	flux
	)

protected

Evaluate the flux at each solution point.

Return the flux vector for the linear advection equation.

Parameters

i	Component of the flux vector to calculate.
physfield	Fields.
flux	Resulting flux.

Definition at line 507 of file MMFAdvection.cpp.

{
    ASSERTL1(flux[0].size() == m_velocity.size(),
             "Dimension of flux array and velocity array do not match");
 
    int i, j;
    int nq = physfield[0].size();
 
    for (i = 0; i < flux.size(); ++i)
    {
        for (j = 0; j < flux[0].size(); ++j)
        {
            Vmath::Vmul(nq, physfield[i], 1, m_velocity[j], 1, flux[i][j], 1);
        }
    }
}

References ASSERTL1, m_velocity, and Vmath::Vmul().

Referenced by v_InitObject().

◆ GetFluxVectorDeAlias()

void Nektar::MMFAdvection::GetFluxVectorDeAlias	(	const Array< OneD, Array< OneD, NekDouble > > &	physfield,
		Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &	flux
	)

protected

Evaluate the flux at each solution point using dealiasing.

◆ GetNormalVelocity()

Array< OneD, NekDouble > & Nektar::MMFAdvection::GetNormalVelocity ( )

protected

Get the normal velocity.

Get the normal velocity for the linear advection equation.

Definition at line 355 of file MMFAdvection.cpp.

{
    // Number of trace (interface) points
    int i;
    int nTracePts = GetTraceNpoints();
 
    // Auxiliary variable to compute the normal velocity
    Array<OneD, NekDouble> tmp(nTracePts);
 
    // Reset the normal velocity
    Vmath::Zero(nTracePts, m_traceVn, 1);
 
    for (i = 0; i < m_velocity.size(); ++i)
    {
        m_fields[0]->ExtractTracePhys(m_velocity[i], tmp);
 
        Vmath::Vvtvp(nTracePts, m_traceNormals[i], 1, tmp, 1, m_traceVn, 1,
                     m_traceVn, 1);
    }
 
    return m_traceVn;
}

References Nektar::SolverUtils::EquationSystem::GetTraceNpoints(), Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::EquationSystem::m_traceNormals, m_traceVn, m_velocity, Vmath::Vvtvp(), and Vmath::Zero().

Referenced by v_InitObject().

◆ Test2Dproblem()

void Nektar::MMFAdvection::Test2Dproblem	(	const NekDouble	time,
		Array< OneD, NekDouble > &	outfield
	)

protected

Definition at line 989 of file MMFAdvection.cpp.

{
    int nq = m_fields[0]->GetNpoints();
 
    Array<OneD, NekDouble> x0(nq);
    Array<OneD, NekDouble> x1(nq);
    Array<OneD, NekDouble> x2(nq);
 
    m_fields[0]->GetCoords(x0, x1, x2);
 
    Array<OneD, NekDouble> u(nq);
 
    for (int i = 0; i < nq; ++i)
    {
        u[i] = cos(m_pi * (x0[i] - m_advx * time)) *
               cos(m_pi * (x1[i] - m_advy * time));
    }
 
    outfield = u;
}

References m_advx, m_advy, Nektar::SolverUtils::EquationSystem::m_fields, and Nektar::SolverUtils::MMFSystem::m_pi.

Referenced by v_EvaluateExactSolution(), and v_SetInitialConditions().

◆ Test3Dproblem()

void Nektar::MMFAdvection::Test3Dproblem	(	const NekDouble	time,
		Array< OneD, NekDouble > &	outfield
	)

protected

Definition at line 1011 of file MMFAdvection.cpp.

{
    int nq = m_fields[0]->GetNpoints();
 
    Array<OneD, NekDouble> x0(nq);
    Array<OneD, NekDouble> x1(nq);
    Array<OneD, NekDouble> x2(nq);
 
    m_fields[0]->GetCoords(x0, x1, x2);
 
    Array<OneD, NekDouble> u(nq);
 
    for (int i = 0; i < nq; ++i)
    {
        u[i] = cos(m_pi * (x0[i] - m_advx * time)) *
               cos(m_pi * (x1[i] - m_advy * time)) *
               cos(m_pi * (x2[i] - m_advz * time));
    }
 
    outfield = u;
}

References m_advx, m_advy, m_advz, Nektar::SolverUtils::EquationSystem::m_fields, and Nektar::SolverUtils::MMFSystem::m_pi.

Referenced by v_EvaluateExactSolution(), and v_SetInitialConditions().

◆ v_DoSolve()

void Nektar::MMFAdvection::v_DoSolve ( void )

overrideprotectedvirtual

Solves an unsteady problem.

Initialises the time integration scheme (as specified in the session file), and perform the time integration.

Reimplemented from Nektar::SolverUtils::UnsteadySystem.

Definition at line 197 of file MMFAdvection.cpp.

{
    ASSERTL0(m_intScheme != nullptr, "No time integration scheme.");
 
    int i, nchk = 1;
    int nvariables = 0;
    int nfields    = m_fields.size();
    int nq         = m_fields[0]->GetNpoints();
 
    if (m_intVariables.empty())
    {
        for (i = 0; i < nfields; ++i)
        {
            m_intVariables.push_back(i);
        }
        nvariables = nfields;
    }
    else
    {
        nvariables = m_intVariables.size();
    }
 
    // Set up wrapper to fields data storage.
    Array<OneD, Array<OneD, NekDouble>> fields(nvariables);
    Array<OneD, Array<OneD, NekDouble>> tmp(nvariables);
 
    // Order storage to list time-integrated fields first.
    for (i = 0; i < nvariables; ++i)
    {
        fields[i] = m_fields[m_intVariables[i]]->GetPhys();
        m_fields[m_intVariables[i]]->SetPhysState(false);
    }
 
    // Initialise time integration scheme
    m_intScheme->InitializeScheme(m_timestep, fields, m_time, m_ode);
 
    // Check uniqueness of checkpoint output
    ASSERTL0((m_checktime == 0.0 && m_checksteps == 0) ||
                 (m_checktime > 0.0 && m_checksteps == 0) ||
                 (m_checktime == 0.0 && m_checksteps > 0),
             "Only one of IO_CheckTime and IO_CheckSteps "
             "should be set!");
 
    LibUtilities::Timer timer;
    bool doCheckTime  = false;
    int step          = 0;
    NekDouble intTime = 0.0;
    NekDouble cpuTime = 0.0;
    NekDouble elapsed = 0.0;
 
    int Ntot, indx;
    // Perform integration in time.
    Ntot = m_checksteps ? m_steps / m_checksteps + 1 : 0;
 
    Array<OneD, NekDouble> dMass(Ntot ? Ntot : 1);
 
    Array<OneD, NekDouble> zeta(nq);
    Array<OneD, Array<OneD, NekDouble>> fieldsprimitive(nvariables);
    for (int i = 0; i < nvariables; ++i)
    {
        fieldsprimitive[i] = Array<OneD, NekDouble>(nq);
    }
 
    while (step < m_steps || m_time < m_fintime - NekConstants::kNekZeroTol)
    {
        timer.Start();
        fields = m_intScheme->TimeIntegrate(step, m_timestep);
        timer.Stop();
 
        m_time += m_timestep;
        elapsed = timer.TimePerTest(1);
        intTime += elapsed;
        cpuTime += elapsed;
 
        // Write out status information
        if (m_infosteps && !((step + 1) % m_infosteps) &&
            m_session->GetComm()->GetRank() == 0)
        {
            std::cout << "Steps: " << std::setw(8) << std::left << step + 1
                      << " "
                      << "Time: " << std::setw(12) << std::left << m_time;
 
            std::stringstream ss;
            ss << cpuTime << "s";
            std::cout << " CPU Time: " << std::setw(8) << std::left << ss.str()
                      << std::endl;
 
            // Masss = h^*
            indx = m_checksteps ? (step + 1) / m_checksteps : 0;
            dMass[indx] =
                (m_fields[0]->Integral(fields[0]) - m_Mass0) / m_Mass0;
 
            std::cout << "dMass = " << std::setw(8) << std::left << dMass[indx]
                      << std::endl;
 
            cpuTime = 0.0;
        }
 
        // Transform data into coefficient space
        for (i = 0; i < nvariables; ++i)
        {
            m_fields[m_intVariables[i]]->SetPhys(fields[i]);
            m_fields[m_intVariables[i]]->FwdTransLocalElmt(
                fields[i], m_fields[m_intVariables[i]]->UpdateCoeffs());
            m_fields[m_intVariables[i]]->SetPhysState(false);
        }
 
        // Write out checkpoint files
        if ((m_checksteps && step && !((step + 1) % m_checksteps)) ||
            doCheckTime)
        {
            Checkpoint_Output(nchk++);
            doCheckTime = false;
        }
 
        // Step advance
        ++step;
    }
 
    std::cout << "dMass = ";
    for (i = 0; i < Ntot; ++i)
    {
        std::cout << dMass[i] << " , ";
    }
    std::cout << std::endl << std::endl;
 
    // Print out summary statistics
    if (m_session->GetComm()->GetRank() == 0)
    {
        if (m_cflSafetyFactor > 0.0)
        {
            std::cout << "CFL safety factor : " << m_cflSafetyFactor
                      << std::endl
                      << "CFL time-step     : " << m_timestep << std::endl;
        }
 
        if (m_session->GetSolverInfo("Driver") != "SteadyState")
        {
            std::cout << "Time-integration  : " << intTime << "s" << std::endl;
        }
    }
 
    for (i = 0; i < nvariables; ++i)
    {
        m_fields[m_intVariables[i]]->SetPhys(fields[i]);
        m_fields[m_intVariables[i]]->SetPhysState(true);
    }
 
    for (i = 0; i < nvariables; ++i)
    {
        m_fields[i]->FwdTrans(m_fields[i]->GetPhys(),
                              m_fields[i]->UpdateCoeffs());
    }
}

◆ v_EvaluateExactSolution()

void Nektar::MMFAdvection::v_EvaluateExactSolution	(	unsigned int	field,
		Array< OneD, NekDouble > &	outfield,
		const NekDouble	time
	)

overrideprotectedvirtual

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 1114 of file MMFAdvection.cpp.

{
    switch (m_TestType)
    {
        case eAdvectionBell:
        {
            AdvectionBellSphere(outfield);
        }
        break;
 
        case eTestPlane:
        {
            Test2Dproblem(time, outfield);
        }
        break;
 
        case eTestPlaneMassConsv:
        {
            AdvectionBellPlane(outfield);
        }
        break;
 
        case eTestCube:
        {
            Test3Dproblem(time, outfield);
        }
        break;
 
        default:
            break;
    }
}

References AdvectionBellPlane(), AdvectionBellSphere(), eAdvectionBell, Nektar::eTestCube, Nektar::eTestPlane, eTestPlaneMassConsv, m_TestType, Test2Dproblem(), and Test3Dproblem().

◆ v_GenerateSummary()

void Nektar::MMFAdvection::v_GenerateSummary ( SolverUtils::SummaryList & s )

overrideprotectedvirtual

Print Summary.

Reimplemented from Nektar::SolverUtils::MMFSystem.

Definition at line 1149 of file MMFAdvection.cpp.

{
    MMFSystem::v_GenerateSummary(s);
    SolverUtils::AddSummaryItem(s, "TestType", TestTypeMap[m_TestType]);
    SolverUtils::AddSummaryItem(s, "Rotation Angle", m_RotAngle);
}

References Nektar::SolverUtils::AddSummaryItem(), m_RotAngle, m_TestType, Nektar::TestTypeMap, and Nektar::SolverUtils::MMFSystem::v_GenerateSummary().

◆ v_InitObject()

void Nektar::MMFAdvection::v_InitObject ( bool DeclareFields = true )

overrideprotectedvirtual

Initialise the object.

Initialisation object for the unsteady linear advection equation.

Reimplemented from Nektar::SolverUtils::AdvectionSystem.

Definition at line 61 of file MMFAdvection.cpp.

{
    // Call to the initialisation object
    UnsteadySystem::v_InitObject(DeclareFields);
 
    int nq       = m_fields[0]->GetNpoints();
    int shapedim = m_fields[0]->GetShapeDimension();
    Array<OneD, Array<OneD, NekDouble>> Anisotropy(shapedim);
    for (int j = 0; j < shapedim; ++j)
    {
        Anisotropy[j] = Array<OneD, NekDouble>(nq, 1.0);
    }
 
    MMFSystem::MMFInitObject(Anisotropy);
 
    // Define TestType
    ASSERTL0(m_session->DefinesSolverInfo("TESTTYPE"),
             "No TESTTYPE defined in session.");
    std::string TestTypeStr = m_session->GetSolverInfo("TESTTYPE");
    for (int i = 0; i < (int)SIZE_TestType; ++i)
    {
        if (boost::iequals(TestTypeMap[i], TestTypeStr))
        {
            m_TestType = (TestType)i;
            break;
        }
    }
 
    m_session->LoadParameter("Angular Frequency", m_waveFreq, m_pi);
    m_session->LoadParameter("Rotational Angle", m_RotAngle, 0.0);
    m_session->LoadParameter("Velocity Projection", m_VelProjection, 0);
 
    // Read the advection velocities from session file
    m_session->LoadParameter("advx", m_advx, 1.0);
    m_session->LoadParameter("advy", m_advy, 1.0);
    m_session->LoadParameter("advz", m_advz, 1.0);
 
    std::vector<std::string> vel;
    vel.push_back("Vx");
    vel.push_back("Vy");
    vel.push_back("Vz");
 
    // Resize the advection velocities vector to dimension of the problem
    vel.resize(m_spacedim);
 
    // Store in the global variable m_velocity the advection velocities
    m_velocity = Array<OneD, Array<OneD, NekDouble>>(m_spacedim);
    for (int k = 0; k < m_spacedim; ++k)
    {
        m_velocity[k] = Array<OneD, NekDouble>(nq);
    }
 
    switch (m_surfaceType)
    {
        case SolverUtils::eSphere:
        case SolverUtils::eTRSphere:
        case SolverUtils::eIrregular:
        case SolverUtils::eNonconvex:
        {
            // true = project velocity onto the tangent plane
            EvaluateAdvectionVelocity(m_velocity);
        }
        break;
 
        case SolverUtils::ePlane:
        case SolverUtils::eCube:
        {
            GetFunction("AdvectionVelocity")->Evaluate(vel, m_velocity);
        }
        break;
 
        default:
            break;
    }
 
    std::cout << "|Velocity vector| = ( " << RootMeanSquare(m_velocity[0])
              << " , " << RootMeanSquare(m_velocity[1]) << " , "
              << RootMeanSquare(m_velocity[2]) << " ) " << std::endl;
 
    // Define the normal velocity fields
    if (m_fields[0]->GetTrace())
    {
        m_traceVn = Array<OneD, NekDouble>(GetTraceNpoints());
    }
 
    std::string advName;
    std::string riemName;
    m_session->LoadSolverInfo("AdvectionType", advName, "WeakDG");
    m_advObject =
        SolverUtils::GetAdvectionFactory().CreateInstance(advName, advName);
    m_advObject->SetFluxVector(&MMFAdvection::GetFluxVector, this);
    m_session->LoadSolverInfo("UpwindType", riemName, "Upwind");
    m_riemannSolver = SolverUtils::GetRiemannSolverFactory().CreateInstance(
        riemName, m_session);
    m_riemannSolver->SetScalar("Vn", &MMFAdvection::GetNormalVelocity, this);
 
    m_advObject->SetRiemannSolver(m_riemannSolver);
    m_advObject->InitObject(m_session, m_fields);
 
    // Compute m_traceVn = n \cdot v
    GetNormalVelocity();
 
    // Compute m_vellc = nabal a^j \cdot m_vel
    ComputeNablaCdotVelocity(m_vellc);
    std::cout << "m_vellc is generated with mag = " << AvgInt(m_vellc)
              << std::endl;
 
    // Compute vel \cdot MF
    ComputeveldotMF(m_veldotMF);
 
    // Modify e^i as v^i e^i
    for (int j = 0; j < m_shapedim; j++)
    {
        for (int k = 0; k < m_spacedim; k++)
        {
            Vmath::Vmul(nq, &m_veldotMF[j][0], 1, &m_movingframes[j][k * nq], 1,
                        &m_movingframes[j][k * nq], 1);
        }
    }
 
    // Reflect it into m_ncdotMFFwd and Bwd
    ComputencdotMF();
 
    // If explicit it computes RHS and PROJECTION for the time integration
    if (m_explicitAdvection)
    {
        m_ode.DefineOdeRhs(&MMFAdvection::DoOdeRhs, this);
        m_ode.DefineProjection(&MMFAdvection::DoOdeProjection, this);
    }
    // Otherwise it gives an error (no implicit integration)
    else
    {
        ASSERTL0(false, "Implicit unsteady Advection not set up.");
    }
}

◆ v_SetInitialConditions()

void Nektar::MMFAdvection::v_SetInitialConditions	(	const NekDouble	initialtime,
		bool	dumpInitialConditions,
		const int	domain
	)

overrideprotectedvirtual

Set the physical fields based on a restart file, or a function describing the initial condition given in the session.

Parameters

initialtime	Time at which to evaluate the function.
dumpInitialConditions	Write the initial condition to file?

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 813 of file MMFAdvection.cpp.

{
    int nq = m_fields[0]->GetNpoints();
 
    Array<OneD, NekDouble> u(nq);
 
    switch (m_TestType)
    {
        case eAdvectionBell:
        {
            AdvectionBellSphere(u);
            m_fields[0]->SetPhys(u);
 
            m_Mass0 = m_fields[0]->Integral(u);
 
            // forward transform to fill the modal coeffs
            for (int i = 0; i < m_fields.size(); ++i)
            {
                m_fields[i]->SetPhysState(true);
                m_fields[i]->FwdTrans(m_fields[i]->GetPhys(),
                                      m_fields[i]->UpdateCoeffs());
            }
        }
        break;
 
        case eTestPlane:
        {
            Test2Dproblem(initialtime, u);
            m_fields[0]->SetPhys(u);
 
            m_Mass0 = m_fields[0]->Integral(u);
 
            // forward transform to fill the modal coeffs
            for (int i = 0; i < m_fields.size(); ++i)
            {
                m_fields[i]->SetPhysState(true);
                m_fields[i]->FwdTrans(m_fields[i]->GetPhys(),
                                      m_fields[i]->UpdateCoeffs());
            }
        }
        break;
 
        case eTestPlaneMassConsv:
        {
            AdvectionBellPlane(u);
            m_fields[0]->SetPhys(u);
 
            m_Mass0 = m_fields[0]->Integral(u);
            std::cout << "m_Mass0 = " << m_Mass0 << std::endl;
 
            // forward transform to fill the modal coeffs
            for (int i = 0; i < m_fields.size(); ++i)
            {
                m_fields[i]->SetPhysState(true);
                m_fields[i]->FwdTrans(m_fields[i]->GetPhys(),
                                      m_fields[i]->UpdateCoeffs());
            }
        }
        break;
 
        case eTestCube:
        {
            Test3Dproblem(initialtime, u);
            m_fields[0]->SetPhys(u);
 
            // forward transform to fill the modal coeffs
            for (int i = 0; i < m_fields.size(); ++i)
            {
                m_fields[i]->SetPhysState(true);
                m_fields[i]->FwdTrans(m_fields[i]->GetPhys(),
                                      m_fields[i]->UpdateCoeffs());
            }
        }
        break;
 
        default:
            break;
    }
 
    if (dumpInitialConditions)
    {
        // dump initial conditions to file
        std::string outname = m_sessionName + "_initial.chk";
        WriteFld(outname);
    }
}

References AdvectionBellPlane(), AdvectionBellSphere(), eAdvectionBell, Nektar::eTestCube, Nektar::eTestPlane, eTestPlaneMassConsv, Nektar::SolverUtils::EquationSystem::m_fields, m_Mass0, Nektar::SolverUtils::EquationSystem::m_sessionName, m_TestType, Test2Dproblem(), Test3Dproblem(), and Nektar::SolverUtils::EquationSystem::WriteFld().

◆ WeakDGDirectionalAdvection()

void Nektar::MMFAdvection::WeakDGDirectionalAdvection	(	const Array< OneD, Array< OneD, NekDouble > > &	InField,
		Array< OneD, Array< OneD, NekDouble > > &	OutField
	)

protected

Definition at line 526 of file MMFAdvection.cpp.

{
    int i, j;
    int ncoeffs         = GetNcoeffs();
    int nTracePointsTot = GetTraceNpoints();
    int nvariables      = m_fields.size();
 
    Array<OneD, Array<OneD, NekDouble>> physfield(nvariables);
 
    // Get the variables in physical space
    // already in physical space
    for (i = 0; i < nvariables; ++i)
    {
        physfield[i] = InField[i];
    }
 
    Array<OneD, Array<OneD, NekDouble>> WeakDeriv(m_shapedim);
    for (i = 0; i < nvariables; ++i)
    {
        for (j = 0; j < m_shapedim; ++j)
        {
            WeakDeriv[j] = Array<OneD, NekDouble>(ncoeffs, 0.0);
 
            // Directional derivation with respect to the j'th moving frame
            // tmp[j] = \nabla \physfield[i] \cdot \mathbf{e}^j
            // Implemented at TriExp::v_IProductWRTDirectionalDerivBase_SumFa
            m_fields[0]->IProductWRTDirectionalDerivBase(
                m_movingframes[j], physfield[i], WeakDeriv[j]);
        }
 
        // Get the numerical flux and add to the modal coeffs
        // if the NumericalFluxs function already includes the
        // normal in the output
 
        Array<OneD, NekDouble> Fwd(nTracePointsTot);
        Array<OneD, NekDouble> Bwd(nTracePointsTot);
 
        Array<OneD, NekDouble> flux(nTracePointsTot, 0.0);
        Array<OneD, NekDouble> fluxFwd(nTracePointsTot);
        Array<OneD, NekDouble> fluxBwd(nTracePointsTot);
 
        // Evaluate numerical flux in physical space which may in
        // general couple all component of vectors
        m_fields[i]->GetFwdBwdTracePhys(physfield[i], Fwd, Bwd);
 
        // evaulate upwinded m_fields[i]
        m_fields[i]->GetTrace()->Upwind(m_traceVn, Fwd, Bwd, flux);
 
        OutField[i] = Array<OneD, NekDouble>(ncoeffs, 0.0);
        for (j = 0; j < m_shapedim; ++j)
        {
            // calculate numflux = (n \cdot MF)*flux
            Vmath::Vmul(nTracePointsTot, &flux[0], 1, &m_ncdotMFFwd[j][0], 1,
                        &fluxFwd[0], 1);
            Vmath::Vmul(nTracePointsTot, &flux[0], 1, &m_ncdotMFBwd[j][0], 1,
                        &fluxBwd[0], 1);
            Vmath::Neg(ncoeffs, WeakDeriv[j], 1);
 
            // FwdBwdtegral because generallize (N \cdot MF)_{FWD} \neq -(N
            // \cdot MF)_{BWD}
            m_fields[i]->AddFwdBwdTraceIntegral(fluxFwd, fluxBwd, WeakDeriv[j]);
            m_fields[i]->SetPhysState(false);
 
            Vmath::Vadd(ncoeffs, &WeakDeriv[j][0], 1, &OutField[i][0], 1,
                        &OutField[i][0], 1);
        }
    }
}

References Nektar::SolverUtils::EquationSystem::GetNcoeffs(), Nektar::SolverUtils::EquationSystem::GetTraceNpoints(), Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::MMFSystem::m_movingframes, Nektar::SolverUtils::MMFSystem::m_ncdotMFBwd, Nektar::SolverUtils::MMFSystem::m_ncdotMFFwd, Nektar::SolverUtils::MMFSystem::m_shapedim, m_traceVn, Vmath::Neg(), Vmath::Vadd(), and Vmath::Vmul().

Referenced by DoOdeRhs().

Friends And Related Function Documentation

◆ MemoryManager< MMFAdvection >

friend class MemoryManager< MMFAdvection >

friend

Definition at line 52 of file MMFAdvection.h.

Member Data Documentation

◆ className

std::string Nektar::MMFAdvection::className

static

Initial value:

=
    SolverUtils::GetEquationSystemFactory().RegisterCreatorFunction(
        "MMFAdvection", MMFAdvection::create, "MMFAdvection equation.")

Name of class.

Definition at line 80 of file MMFAdvection.h.

◆ m_advx

NekDouble Nektar::MMFAdvection::m_advx

protected

Definition at line 85 of file MMFAdvection.h.

Referenced by Test2Dproblem(), Test3Dproblem(), and v_InitObject().

◆ m_advy

NekDouble Nektar::MMFAdvection::m_advy

protected

Definition at line 85 of file MMFAdvection.h.

Referenced by Test2Dproblem(), Test3Dproblem(), and v_InitObject().

◆ m_advz

NekDouble Nektar::MMFAdvection::m_advz

protected

Definition at line 85 of file MMFAdvection.h.

Referenced by Test3Dproblem(), and v_InitObject().

◆ m_Mass0

NekDouble Nektar::MMFAdvection::m_Mass0

protected

Definition at line 87 of file MMFAdvection.h.

Referenced by v_DoSolve(), and v_SetInitialConditions().

◆ m_riemannSolver

SolverUtils::RiemannSolverSharedPtr Nektar::MMFAdvection::m_riemannSolver

protected

Definition at line 83 of file MMFAdvection.h.

Referenced by v_InitObject().

◆ m_RotAngle

NekDouble Nektar::MMFAdvection::m_RotAngle

protected

Definition at line 86 of file MMFAdvection.h.

Referenced by EvaluateAdvectionVelocity(), v_GenerateSummary(), and v_InitObject().

◆ m_TestType

TestType Nektar::MMFAdvection::m_TestType

protected

Definition at line 84 of file MMFAdvection.h.

Referenced by v_EvaluateExactSolution(), v_GenerateSummary(), v_InitObject(), and v_SetInitialConditions().

◆ m_traceVn

Array<OneD, NekDouble> Nektar::MMFAdvection::m_traceVn

protected

Definition at line 90 of file MMFAdvection.h.

Referenced by GetNormalVelocity(), v_InitObject(), and WeakDGDirectionalAdvection().

◆ m_veldotMF

Array<OneD, Array<OneD, NekDouble> > Nektar::MMFAdvection::m_veldotMF

protected

Definition at line 91 of file MMFAdvection.h.

Referenced by v_InitObject().

◆ m_vellc

Array<OneD, NekDouble> Nektar::MMFAdvection::m_vellc

protected

Definition at line 92 of file MMFAdvection.h.

Referenced by v_InitObject().

◆ m_velocity

Array<OneD, Array<OneD, NekDouble> > Nektar::MMFAdvection::m_velocity

protected

Definition at line 89 of file MMFAdvection.h.

Referenced by ComputeNablaCdotVelocity(), ComputeveldotMF(), DoOdeRhs(), EvaluateAdvectionVelocity(), GetFluxVector(), GetNormalVelocity(), and v_InitObject().

◆ m_VelProjection

int Nektar::MMFAdvection::m_VelProjection

protected

Definition at line 88 of file MMFAdvection.h.

Referenced by EvaluateAdvectionVelocity(), and v_InitObject().

◆ m_waveFreq

NekDouble Nektar::MMFAdvection::m_waveFreq

protected

Definition at line 86 of file MMFAdvection.h.

Referenced by EvaluateAdvectionVelocity(), and v_InitObject().

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MMFAdvection()

◆ ~MMFAdvection()

Member Function Documentation

◆ AdvectionBellPlane()

◆ AdvectionBellSphere()

◆ ComputeCirculatingArclength()

◆ ComputeNablaCdotVelocity()

◆ ComputeveldotMF()

◆ create()

◆ DoOdeProjection()

◆ DoOdeRhs()

◆ EvaluateAdvectionVelocity()

◆ GetFluxVector()

◆ GetFluxVectorDeAlias()

◆ GetNormalVelocity()

◆ Test2Dproblem()

◆ Test3Dproblem()

◆ v_DoSolve()

◆ v_EvaluateExactSolution()

◆ v_GenerateSummary()

◆ v_InitObject()

◆ v_SetInitialConditions()

◆ WeakDGDirectionalAdvection()

Friends And Related Function Documentation

◆ MemoryManager< MMFAdvection >

Member Data Documentation

◆ className

◆ m_advx

◆ m_advy

◆ m_advz

◆ m_Mass0

◆ m_riemannSolver

◆ m_RotAngle

◆ m_TestType

◆ m_traceVn

◆ m_veldotMF

◆ m_vellc

◆ m_velocity

◆ m_VelProjection

◆ m_waveFreq